The field of digital data compression and in particular digital image compression has attracted great interest for some time.
In the field of digital image compression, many different techniques have been utilised. In particular, one popular technique is the JPEG standard which utilises the Discrete Cosine Transform to transform standard size blocks of an image into corresponding cosine components. In this respect, the higher frequency cosine components are heavily quantised so as to assist in obtaining substantial compression factors. The heavy quantisation is an example of a "lossy" technique of image compression. The JPEG standard also provides for the subsequent "lossless" compression of the transformed coefficients.
Recently, the field of wavelet transforms has gained great attention as an alternative form of data compression. The wavelet transform has been found to be highly suitable in representing data having discontinuities such as sharp edges. Such discontinuities are often present in image data or the like.
Although the preferred embodiments of the present invention will be described with reference to the compression of image data, it will be readily evident that the preferred embodiment is not limited thereto. For examples of the many different applications of Wavelet analysis to signals, reference is made to a survey article entitled "Wavelet Analysis" by Bruce et. al. appearing in IEEE Spectrum, October 1996 page 26-35. For a discussion of the different applications of wavelets in computer graphics, reference is made to "Wavelets for Computer Graphics", I. Stollinitz et. al. published 1996 by Morgan Kaufmann Publishers, Inc.
Unfortunately, the standard techniques are normally ideally utilised on wavelet data having dimensions that are normally a binary power of 2. As such, this data represents an idealised case in that not all image data will be conveniently sized to be a power of 2 especially where multilevel Wavelet decompositions are carried out. Given that high degrees of compression are the objective, it is unclear how one should deal with image data that does not fit into a certain number of limited sizes.